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Mathematics 21 Online
OpenStudy (anonymous):

is there anyway to integrate this without using by parts? \int (4x)/(x+1)^2

OpenStudy (amistre64):

maybe do a partial frac decomp?

OpenStudy (amistre64):

or expand the denom and see what its derivative is

OpenStudy (amistre64):

x^2 +2x +1 2x + 2 4x +2 -2 = 2(2x+2-2) might be an idea

OpenStudy (amistre64):

well, +4-4 ... but same idea

OpenStudy (anonymous):

I did expan the denom, partial fraction will not work because both fractions will have x+1 as the denom

OpenStudy (phi):

you could use u= (x+1)

OpenStudy (anonymous):

but du = 1, our number is 4x

OpenStudy (anonymous):

*numerator

OpenStudy (amistre64):

\[\frac{4x}{x^2+2x+1}=\frac{2(2x+2-2)}{x^2+2x+1}=2*\frac{2x+2}{(x+1)^2}*\frac{-2}{(x+1)^2}\]

OpenStudy (phi):

(4x)/(x+1)^2 dx --> 4(u-1) u^-2 du 4u^(-1) - 4u^(-2) du

OpenStudy (amistre64):

umm, mine should have addition in it not * lol

OpenStudy (amistre64):

\[\frac{4x}{x^2+2x+1}=\frac{2(2x+2-2)}{x^2+2x+1}=2 \left( \frac{2x+2}{(x+1)^2}+\frac{-2}{(x+1)^2}\right)\]

OpenStudy (amistre64):

soo, if we integrate :) 2( ln (x+1)^2 +2(x+1)^-1 +C)

OpenStudy (amistre64):

maybe

OpenStudy (anonymous):

ok, thx amistre....got it. thanks!!!

OpenStudy (amistre64):

http://www.wolframalpha.com/input/?i=derivative+4ln%28x%2B1%29+%2B+4%2F%28x%2B1%29 the wolf likes it :)

OpenStudy (anonymous):

i didn't play around with the algebra enough. much appreciated.

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